is_user_logged_in() not working in AJAX validation call

The answer is right in your question and in the error message.

Take a look at this part of your code:

public function validate_current_password( $current_password = NULL ) {
    // Check if logged in
    if ( !is_user_loggged_in() ) {
        return $this->get_error( 'not_logged_in' );
    }

    // Rest of validation...
}

You have a typo in there. You use is_user_loggged_in() and there really is no such function. It should be is_user_logged_in() (only two ‘g’s).